PetscDTEnumPerm#
Get a permutation of n integers from its encoding into the integers [0, n!) as a sequence of swaps.
Input Parameters#
n - a non-negative integer (see note about limits below)
k - an integer in [0, n!)
Output Parameters#
perm - the permuted list of the integers [0, …, n-1]
isOdd - if not
NULL, returns whether the permutation used an even or odd number of swaps.
Notes#
A permutation can be described by the operations that convert the lists [0, 1, …, n-1] into the permutation, by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in some position j >= i. This swap is encoded as the difference (j - i). The difference d_i at step i is less than (n - i). This sequence of n-1 differences [d_0, …, d_{n-2}] is encoded as the number (n-1)! * d_0 + (n-2)! * d_1 + … + 1! * d_{n-2}.
Limited to n such that n! can be represented by PetscInt, which is 12 if PetscInt is a signed 32-bit integer and 20 if PetscInt is a signed 64-bit integer.
See Also#
PetscDTFactorial(), PetscDTFactorialInt(), PetscDTBinomial(), PetscDTBinomialInt(), PetscDTPermIndex()
Level#
intermediate
Location#
Index of all DT routines
Table of Contents for all manual pages
Index of all manual pages